On the Equivalence of Weak- and Cyclic-Monotonicity

39 Pages Posted: 22 Jul 2019 Last revised: 5 Aug 2019

See all articles by Alexey I. Kushnir

Alexey I. Kushnir

Carnegie Mellon University - David A. Tepper School of Business

Lev Lokutsievskiy

Steklov Mathematical Institute of RAS; Moscow Lomonosov State University

Date Written: August 3, 2019

Abstract

We provide an approach to studying the equivalence of weak- and cyclic-monotonicity conditions in convex and non-convex domains with a finite set of outcomes. Using this approach, we establish the new equivalence results for gross-substitutes preferences and single-peaked preferences on posets. We also provide novel applications of the equivalence result to problems in mechanism design, spatial allocation, revealed preference theory, and producer choice theory.

Keywords: weak-monotonicity, cyclic-monotonicity, non-convex domain, mechanism design, spatial allocation, revealed preference theory, producer choice theory, algebraic topology, homology

JEL Classification: D11, D21, D82

Suggested Citation

Kushnir, Alexey I. and Lokutsievskiy, Lev, On the Equivalence of Weak- and Cyclic-Monotonicity (August 3, 2019). Available at SSRN: https://ssrn.com/abstract=3422846 or http://dx.doi.org/10.2139/ssrn.3422846

Alexey I. Kushnir (Contact Author)

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

Lev Lokutsievskiy

Steklov Mathematical Institute of RAS ( email )

Gubkina St. 8
Moscow, 117966
Russia

HOME PAGE: http://www.mathnet.ru/php/person.phtml?&personid=27986&option_lang=eng

Moscow Lomonosov State University ( email )

SP-1, Leninskie Gory
Moscow, 119991
Russia

HOME PAGE: http://www.mathnet.ru/php/person.phtml?&personid=27986&option_lang=eng

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